Relevance of semi‐core‐valence interaction for exact exchange calculations for group IVA, IIIA–VA, and IIB–VIA semiconductors

Abstract

The importance of the semi‐core‐valence interaction for plane‐wave pseudopotential calculations with exact exchange is investigated for group IVA, IIIA–VA, and IIB–VIA semiconductors. Results for different valence spaces, either omitting or including the semi‐core d‐ and/or the semi‐core sp‐states, are compared with full‐potential LAPW all‐electron data. It is found that for group IIB, IIIA, and IVA elements only the valence space including all semi‐core states leads to accurate band structures. In fact, no real improvement over the minimum valence space is obtained for group IIIA and IVA elements, if only the semi‐core d‐states are taken into account. The particular relevance of the semi‐core sp‐states arises from the nonlocality of the exact exchange, which makes the exchange potential in the valence region sensitive to orbital structures located in the semi‐core region (such as the nodes of the valence states). In contrast, even the valence space without any semi‐core states yields very accurate results in the case of group VA elements, indicating the onset of the decoupling of the M‐shell from the valence states. To deal with valence spaces including all semi‐core states a proper construction of pseudopotentials is essential. While usually the energetically lowest state in the valence space is utilized to generate the pseudopotential for the corresponding angular momentum, it is shown here that this procedure can induce significant errors, when applied in the presence of semi‐core states. Accurate results are only obtained, if the pseudopotentials are generated from the (occupied) valence states (under the constraint that the corresponding pseudoorbitals have one node), the reason being that the norm‐conservation of the valence states is more important for the electronic structure of the bulk than that of the semi‐core states. As a byproduct, it is shown that highly accurate pseudopotential results can also be obtained for solid Ne. © 2016 Wiley Periodicals, Inc.